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Point K(8,-5) lies on the circle x^2 +y^2 - 12x - 6y - 23. find the equation of the tangent at K.

First, find the centre of the circle. Since we know the equation of the circle, we know that the centre (-g,-f) comes from the part of the equation -12x-6y, where -12=2g and -6=2f. Therefore, to get the cent...
CM
Answered by Catriona M. • Maths tutor
2791 Views

Calculate the rate of change of d(t )=2/(3t), t ≠ 0, when t=6.

When a question asks for rate of change, this means you need to differentiate the equation. First you need to put the equation into differentiable a form ie, with the no variables on the denominator: f(t) = ...
LI
Answered by Lucy I. • Maths tutor
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An exoplanet, 0.01% the mass of the Sun, orbits a star 2 times the mass of the Sun at a distance of 1AU = 1.5x10^8 km. Using Newton's Law of Universal Gravitation, determine the force between the exoplanet and the star. Mass of Sun = 2x10^30kg.

This question is not particularly tricky as long as it is read carefully. First, calculate the masses of the Star and the Exoplanet. Double the mass to find the star mass (M). To find the planet mass, multip...
TR
Answered by Thomas R. • Physics tutor
2640 Views

Two cables hold a mass of 100kg, joining in the middle of the top of the mass. Two helicopters lift a cable each and hover so that the height of the mass is constant. Each cable makes an angle of 57° with the normal. Find the tension in each cable.

Once you note that the height is constant, the key thing to remember here is that there is no unbalanced force acting on the mass. By this, I mean that since the mass is not accelerating (it is actually at r...
JK
Answered by Joseph K. • Physics tutor
2927 Views

How do I find the dot product of two 3-dimensional vectors

Example; Let vector v = (2,5,2) and vector u = (1,-2,3),then u · v = [(2 x 1) + (5 x -2) + (2 x 3)] = [2 -10 + 6] = -2 As the workings hopefully make clear in the line above, the general formula for the scal...
TV
Answered by Theo V. • Maths tutor
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